Hyperbolic polynomial diffeomorphisms of \(\mathbb C^2\). II: Hubbard trees
This paper is a continuation of Part I [\textit{Y. Ishii}, Adv. Math. 218, No. 2, 417--464 (2008; Zbl 1136.37028)]. The purpose of the current paper is to construct an object analogous to a Hubbard tree consisting of a pair of trees decorated with loops and a pair of maps between them for certain complex Hénon map or, more generally, a polynomial diffeomorphism \(f\) of \(\mathbb{C}^2\). The authors also show that a Hubbard tree gives a topological model for the dynamics of \(f\) on its Julia set in terms of its finite data. Recall that a Hubbard tree describes how the orbits of the critical points of a polynomial are sitting inside its Julia set.
scientific article; zbMATH DE number 5518752